For selected screw lead L, revolutions n and target traverse speed v, ideal travel is Ln, required speed is 1000v/L rpm when v is in m/min, and travel rate is 1000v/60 mm/s. Selected loss is 100−η.
Ideal Ball-Screw Traverse Kinematics
Explore ideal ball-screw lead, travel, required speed and selected efficiency loss.
Equation Used
- The screw rotates on a fixed axis and the nut is constrained against rotation.
- One revolution advances the nut by one selected lead.
- Traverse speed is constant and converted from m/min.
- Selected efficiency is reported only as 100−η; loads, torque, power, friction and life are excluded.
The displayed closed ball loop is a normalized topology reference, not a detailed raceway design.
Guided nut and recirculation reference
The animation shows a fixed-axis rotating screw, a rotation-constrained carriage nut on parallel guides, and a closed normalized return circuit moving with the nut. The presentation advances one lead during one screw revolution.
The ball loop is a topology reference, not a manufacturer-specific internal raceway or contact-angle model.
What the calculator determines
Select screw lead, revolutions, target traverse speed and a selected efficiency. Outputs are ideal travel, required rpm, ideal travel rate and selected loss percentage.
Efficiency does not change the ideal lead relationship in this calculator; no input torque, load or power is supplied.
Ideal traverse identities
Travel = Ln, required rpm = 1000v/L, travel rate = 1000v/60, and selected loss = 100−η. One revolution advances one lead for an ideal no-slip screw pair.
Selected-input example
For L = 10 mm/rev, n = 1 rev, v = 30 m/min and η = 90%, ideal travel is 10 mm, required speed is 3,000 rpm, travel rate is 500 mm/s and selected loss is 10%.
Scope and design boundary
Real ball-screw selection requires axial load, duty cycle, preload, accuracy class, critical speed, buckling, support conditions, lubrication and life calculations. Efficiency can affect torque and power, neither of which is modeled here.
Unsupported accuracy, service-life, lubrication-quantity, maintenance and application claims are removed.
Questions
Does efficiency reduce travel per revolution?
Not in this ideal kinematic model; the nut still advances one lead per revolution.
Why does lower lead require more rpm at the same traverse speed?
Each revolution produces less axial travel.
Is the ball loop a detailed raceway design?
No. It only identifies a closed recirculation topology.
Can this select a ball screw?
No.
References & Further Reading
- Wikipedia contributors. Ball screw. Wikipedia
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